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Functions | |
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Functions | |
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Graphing Functions Using Calculators and Computer Algebra Systems | |
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New Functions from Old | |
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Families of Functions | |
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Inverse Functions Inverse Trigonometric Functions | |
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Exponential and Logarithmic Functions | |
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Mathematical Models | |
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Parametric Equations 86 | |
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Limits And Continuity | |
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Limits (An Intuitive Approach) | |
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Computing Limits | |
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Limits at Infinity End Behavior of a Function | |
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Limits (Discussed More Rigorously) | |
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Continuity | |
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Continuity of Trigonometric and Inverse Functions | |
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The Derivative | |
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Tangent Lines, Velocity, and General Rates of Change | |
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The Derivative Function | |
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Techniques of Differentiation | |
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The Product and Quotient Rules | |
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Derivatives of Trigonometric Functions | |
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The Chain Rule | |
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Related Rates | |
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Local Linear Approximation Differentials | |
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Exponential, Logarithmic, And Inverse Trigonometric Functions | |
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Implicit Differentiation | |
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Derivatives of Logarithmic Functions | |
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Derivatives of Exponential and Inverse Trigonometric Functions | |
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L'H(pital's Rule Indeterminate Forms | |
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The Derivative In Graphing And Applications | |
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Analysis of Functions I: Increase, Decrease, and Concavity | |
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Analysis of Functions II: Relative Extrema Graphing Polynomials | |
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More on Curve Sketching: Rational Functions Curves with Cusps and Vertical Tangent Lines Using Technology | |
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Absolute Maxima and Minima | |
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Applied Maximum and Minimum Problems | |
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Newton's Method | |
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Rolle's Theorem Mean-Value Theorem | |
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Rectilinear Motion | |
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Integration | |
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An Overview of the Area Problem | |
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The Indefinite Integral | |
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Integration by Substitution | |
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The Definition of Area as a Limit Sigma Notation | |
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The Definite Integral | |
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The Fundamental Theorem of Calculus | |
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Rectilinear Motion Revisited Using Integration | |
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Evaluating Definite Integrals by Substitution | |
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Applications Of The Definite Integral In Geometry, Science, And Engineering | |
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Area Between Two Curves | |
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Volumes by Slicing Disks and Washers | |
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Volumes by Cylindrical Shells | |
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Length of a Plane Curve | |
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Area of a Surface of Revolution | |
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Average Value of a Function and its Applications | |
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Work | |
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Fluid Pressure and Force | |
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Hyperbolic Functions and Hanging Cables | |
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Principles Of Integral Evaluation | |
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An Overview of Integration Methods | |
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Integration by Parts | |
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Trigonometric Integrals | |
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Trigonometric Substitutions | |
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Integrating Rational Functions by Partial Fractions | |
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Using Computer Algebra Systems and Tables of Integrals | |
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Numerical Integration Simpson's Rule | |
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Improper Integrals | |
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Mathematical Modeling With Differential Equations | |
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First-Order Differential Equations and Applications | |
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Slope Fields Euler's Method | |
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Modeling with First-Order Differential Equations | |
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Second-Order Linear Homogeneous Differential Equations The Vibrating Spring | |
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Infinite Series | |
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Sequences | |
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Monotone Sequences | |
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Infinite Series | |
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Convergence Tests | |
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The Comparison, Ratio, and Root Tests | |
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Alternating | |